Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sseq12d | Unicode version |
Description: An equality deduction for the subclass relationship. (Contributed by NM, 31-May-1999.) |
Ref | Expression |
---|---|
sseq1d.1 | |
sseq12d.2 |
Ref | Expression |
---|---|
sseq12d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq1d.1 | . . 3 | |
2 | 1 | sseq1d 2972 | . 2 |
3 | sseq12d.2 | . . 3 | |
4 | 3 | sseq2d 2973 | . 2 |
5 | 2, 4 | bitrd 177 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 wss 2917 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-in 2924 df-ss 2931 |
This theorem is referenced by: 3sstr3d 2987 3sstr4d 2988 ssdifeq0 3305 relcnvtr 4840 rdgisucinc 5972 nnaword 6084 nnawordi 6088 |
Copyright terms: Public domain | W3C validator |